The heart of the fiber optic rotation rate sensor or gyroscope (hereafter, simply FOG) is well known in the art is the Sagnac interferometer, briefly illustrated in FIG. 1. The Sagnac interferometer in its simplest form consists of a single directional coupler 108, e.g. a beam splitter, and an optical path that in our case amounts to a length of optical fiber formed into a loop 20, 1 turn or multiple turns, respectively. The directional coupler 108 is used to split an impinging light wave derived from a light source 100 into two waves, but it can also be used to combine two waves, or in other words, interfere two waves. The directional coupler in a Sagnac interferometer will do both. After the directional coupler 108 splits the light wave, the resulting two waves enter opposite ends of the optical fiber loop 20 and propagate in opposite directions through the optical fiber loop 20, pass through each other, emerge from the fiber, and are combined by the same directional coupler 108. The optical power of the combined waves depends upon the phase difference between the two interfering waves. The phase shift is related to the rotation rate of the fiber loop according to the Sagnac effect, and can be expressed as,
  Δϕ  =                    2        ⁢        π        ⁢                                  ⁢        LD                    λ        ⁢                                  ⁢        c              ⁢    Ω  where L is the length of the fiber in the loop, D is the diameter of the loop, λ and c are the wavelength and speed of the light in vacuum, respectively. The diameter D of the loop is usually constrained by the application, and is typically between 1 and 6 inches. Winding the optical fiber (hereafter referred to as simply fiber) into a multiturn coil can increase the length of fiber, L. while maintaining a manageable diameter D. Typical lengths are between 0.05 and 5 km. The packaging volume, of course, imposes a limit on the length of the coil of optical fiber. The outside diameter (OD) and the height of the fiber coil are generally limited by the space allocated by the system designer. The fiber length is limited by the number of turns of fiber that will fit on each layer and the number of layers that will fit in the package. The outside layer will provide the most signal because it has the largest diameter as well as the largest length of fiber per layer. Each successive inner layer becomes smaller in both diameter and fiber length per layer. Reducing the fiber diameter increases the length of fiber that will fit into the space allotted, but the fiber becomes more delicate and increasingly difficult to wind accurately as the size is reduced. Accurate winding helps to ensure tight packing of the fiber, and is intended to reduce sensitivity to environmental changes such as temperature and pressure, as is well known.
Operation of the FOG is based on the Sagnac effect as aforesaid. The way that the FOG enhances the sensitivity to rotation is via increasing the total phase shift between the counter-propagating waves by making them follow a long fiber path—typical gyro fiber lengths are 50 meters to a few kilometers. The basic FOG architecture as illustrated in FIG. 1 is called the “Minimum” or “reciprocal” configuration. This has been the optical architecture of choice for all medium- and high-accuracy fiber optic gyroscopes since the 1980s (Ulrich 1980). The reason is that the clockwise and counter-clockwise waves traverse almost identical paths so that common-mode errors tend to cancel each other. Soon after Ulrich's proposal, the group led by Arditty and Lefevre in France proposed the hybrid architecture, which combines fiber components with an integrated optic Y-junction fabricated with lithium niobate waveguides (Arditty et al. 1984; Lefevre et al, 1985). In a FOG, the light from the source is split by a splitter, and the two light waves thus created enter opposite ends of an optical fiber that is wound into a coil, they pass through each other as they counter propagate through the fiber and return to the splitter where the two waves are combined, and the combined waves are directed to a detector.
A cylindrical fiber coil is often referred to in terms of its diameter, D, and the length, L, of the fiber. The phase difference between the combined waves is proportional to the LD product times the rotation rate according to the Sagnac effect. The main benefit of using an optical fiber is that L can be quite large while D can be a manageable size. Because the two waves counter-propagate through the same fiber, a tremendous error reduction is gained regarding perturbations of the fiber. This reduction is not perfect because the two waves traverse a given section of fiber at different times.
The FOG has been very successful in a limited number of applications. These include applications where the fiber coil is not subjected to large variations in temperature and where the FOG can be made quite large. In some applications with limited temperature range, where the power requirements and startup requirements allow, the fiber-optic coil is actually temperature controlled. In such cases the fiber can be made very long and the rotation-rate signal made large compared to noise to improve the rotation-rate measurement. The increased fiber length only works in benign conditions or when the temperature is controlled because errors due to environmental perturbations scale with length. Clever winding techniques have, however, reduced the impact of time varying strain gradients in the coil, but further improvement is necessary for the FOG to reach its full potential.
If the FOG is designed and constructed well, its ability to accurately measure rotation rate is limited by the stability of the present state-of-the-art fiber coil as it is subjected to a changing environment. Generally, the fiber coil is a composite structure of glass and a variety of plastics including adhesive to hold it together. The signal in the FOG increases with the diameter of the coil and also with the number of turns of fiber in the coil. Increasing the diameter of the coil has the obvious problem of increasing the size of the FOG. The diameter of the coil is made to be as large as is acceptable in the application for which the FOG is intended. Increasing the number of turns of fiber also increases the size of the coil, and it reduces the coil stability. Adding more turns either means increasing the axial dimension of the coil or adding more layers of fiber. The plastic in the coil expands with temperature much faster than the glass fiber. The result is that the plastic strains the fiber in a way that varies from layer to layer. This causes a time-varying strain gradient if the temperature is varying in time, and thereby causes a measurement error. In some cases the error can be measured and compensated for to some extent; in other cases it is not easy to distinguish the error from rotation-rate measurement, and it is not possible to compensate for the error.